Leech Constellations of Construction-A Lattices
The problem of communicating over the additive white Gaussian noise (AWGN) channel with lattice codes is addressed in this paper. Theoretically, Voronoi constellations have proved to yield very powerful lattice codes when the fine/coding lattice is AWGN-good and the coarse/shaping lattice has an opt...
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| creator | di Pietro, Nicola Boutros, Joseph J |
| description | The problem of communicating over the additive white Gaussian noise (AWGN)
channel with lattice codes is addressed in this paper. Theoretically, Voronoi
constellations have proved to yield very powerful lattice codes when the
fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal
shaping gain. However, achieving Shannon capacity with these premises and
practically implementable encoding algorithms is in general not an easy task.
In this work, a new way to encode and demap Construction-A Voronoi lattice
codes is presented. As a meaningful application of this scheme, the second part
of the paper is focused on Leech constellations of low-density Construction-A
(LDA) lattices: LDA Voronoi lattice codes are presented whose numerically
measured waterfall region is situated at less than 0.8 dB from Shannon
capacity. These LDA lattice codes are based on dual-diagonal nonbinary
low-density parity-check codes. With this choice, encoding, iterative decoding,
and demapping have all linear complexity in the blocklength. |
| doi_str_mv | 10.48550/arxiv.1611.04417 |
| format | Article |
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channel with lattice codes is addressed in this paper. Theoretically, Voronoi
constellations have proved to yield very powerful lattice codes when the
fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal
shaping gain. However, achieving Shannon capacity with these premises and
practically implementable encoding algorithms is in general not an easy task.
In this work, a new way to encode and demap Construction-A Voronoi lattice
codes is presented. As a meaningful application of this scheme, the second part
of the paper is focused on Leech constellations of low-density Construction-A
(LDA) lattices: LDA Voronoi lattice codes are presented whose numerically
measured waterfall region is situated at less than 0.8 dB from Shannon
capacity. These LDA lattice codes are based on dual-diagonal nonbinary
low-density parity-check codes. With this choice, encoding, iterative decoding,
and demapping have all linear complexity in the blocklength.</description><identifier>DOI: 10.48550/arxiv.1611.04417</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2016-11</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1611.04417$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1611.04417$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>di Pietro, Nicola</creatorcontrib><creatorcontrib>Boutros, Joseph J</creatorcontrib><title>Leech Constellations of Construction-A Lattices</title><description>The problem of communicating over the additive white Gaussian noise (AWGN)
channel with lattice codes is addressed in this paper. Theoretically, Voronoi
constellations have proved to yield very powerful lattice codes when the
fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal
shaping gain. However, achieving Shannon capacity with these premises and
practically implementable encoding algorithms is in general not an easy task.
In this work, a new way to encode and demap Construction-A Voronoi lattice
codes is presented. As a meaningful application of this scheme, the second part
of the paper is focused on Leech constellations of low-density Construction-A
(LDA) lattices: LDA Voronoi lattice codes are presented whose numerically
measured waterfall region is situated at less than 0.8 dB from Shannon
capacity. These LDA lattice codes are based on dual-diagonal nonbinary
low-density parity-check codes. With this choice, encoding, iterative decoding,
and demapping have all linear complexity in the blocklength.</description><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjrsOgkAURLexMOgHWMkPAHtZdhdKQnwlJDb05LKPSIJiAI3-vTwsJjM5xeQQsgPqRzHnNMDuU799EAA-jSKQaxLkxqibm7WPfjBNg0M9Lre1C-leagJe6uY4DLUy_YasLDa92f7bIcXxUGRnL7-eLlmaeyik9BCF4BBblmidSKx4IjkPmdCAkiprR1DFFGwVMs0NZxTGhEqHCVaRjIE5ZL_czsbls6vv2H3LybyczdkPzIU9BA</recordid><startdate>20161114</startdate><enddate>20161114</enddate><creator>di Pietro, Nicola</creator><creator>Boutros, Joseph J</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20161114</creationdate><title>Leech Constellations of Construction-A Lattices</title><author>di Pietro, Nicola ; Boutros, Joseph J</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-aa66518f39dd97ab59755236d1a70cffb59b801fb23d5e53015302cd29ab47813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>di Pietro, Nicola</creatorcontrib><creatorcontrib>Boutros, Joseph J</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>di Pietro, Nicola</au><au>Boutros, Joseph J</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Leech Constellations of Construction-A Lattices</atitle><date>2016-11-14</date><risdate>2016</risdate><abstract>The problem of communicating over the additive white Gaussian noise (AWGN)
channel with lattice codes is addressed in this paper. Theoretically, Voronoi
constellations have proved to yield very powerful lattice codes when the
fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal
shaping gain. However, achieving Shannon capacity with these premises and
practically implementable encoding algorithms is in general not an easy task.
In this work, a new way to encode and demap Construction-A Voronoi lattice
codes is presented. As a meaningful application of this scheme, the second part
of the paper is focused on Leech constellations of low-density Construction-A
(LDA) lattices: LDA Voronoi lattice codes are presented whose numerically
measured waterfall region is situated at less than 0.8 dB from Shannon
capacity. These LDA lattice codes are based on dual-diagonal nonbinary
low-density parity-check codes. With this choice, encoding, iterative decoding,
and demapping have all linear complexity in the blocklength.</abstract><doi>10.48550/arxiv.1611.04417</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | Leech Constellations of Construction-A Lattices |
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